On a fluid-structure interaction problem for plaque growth: cylindrical domain

Abstract

This paper concerns a free-boundary fluid-structure interaction problem for plaque growth proposed by Yang et al. (2016) [50] with additional viscoelastic effects, which was also investigated by the authors (2021) [1]. Compared to it, the problem is posed in a cylindrical domain with ninety-degree contact angles, which brings additional difficulties when we deal with the linearization of the system. By a reflection argument, we obtain the existence and uniqueness of strong solutions to the model problems for the linear systems, which are then shown to be well-posed in a cylindrical (annular) domain via a localization procedure. Finally, we prove that the full nonlinear system admits a unique strong solution locally with the aid of the contraction mapping principle.